CPR X NON ADHERENCE TO ATC CLRNC HAD LTSS FROM CPR Y.

Narrative

CPR X; C650; ON 050 DEG HDG FOR HPN TOLD TO GO RNAV DIRECT BREZY INTXN THEN ON COURSE. CPR Y; AC69; 5 NM INTRAIL TO CPR X ON 050 DEG HDG ALSO. (BREZY WAS ABOUT A 060 DEG HDG FROM CPR X POS.) I LOOKED AWAY. WHEN I LOOKED BACK THE 2 ACFT HAD JUST PASSED. I ASKED THE CPR X HIS HDG. IT WAS 170 DEGS (WRONG DIRECTION FOR BREZY). I TURNED HIM L AND DSNDED CPR Y TO 2000 FT. I CALLED TFC FOR THE CPR Y; THEN CLRED HIM FOR APCH TO TEB. THE 2 ACFT PASSED EACH OTHER AGAIN (SEPARATED THIS TIME). SUPPLEMENTAL INFO FROM ACN 266805: WHILE BEING VECTORED AFTER DEP; ATC CLRED US DIRECT BREZY. UTILIZING THE FMS; WENT TOWARD THE INDICATED POINT. ATC THEN QUESTIONED OUR HDG AND ADJUSTED (160 DEGS) IT TO SEND US TOWARD BREZY. DURING THIS TIME; WE HAD MULTIPLE TCASII ALERTS; COPLT WAS DOING CHKLISTS AND OBTAINING ATIS DURING THIS SHORT FLT (30 NM). BETTER POSITIONAL AWARENESS ON MY PART COULD HAVE PREVENTED THIS; AS COULD A QUICK XCHK BY PNF. FMS WAS SUBSEQUENTLY FOUND TO BE TOTALLY 'OUT TO LUNCH' AND WRITTEN UP BY AIR CREW FOR MAINT ACTION.